central limit theorem

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cen·tral lim·it the·o·rem

the sum (or average) of n realizations of the same process, provided only that it has a finite variance, will approach the gaussian distribution as n becomes indefinitely large. This theory provides a broad warrant for the use of normal theory even for nongaussian data. In the form stated here, it constitutes the classical version; more general versions allow serious relaxation of the usual assumptions.
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Alternatively, by the asymptotic normality of the MLE, the approximate 100(1 - [alpha])% CIs for [mu] and [sigma] can be obtained as
The main contribution of this paper was in the establishment of asymptotic normality when the Hurst parameter satisfied H [member of] (1/2,1).
Heinrich and Prokesova (2010) proved that if P is a stationary point process, with milder mixing conditions than the ones required for the asymptotic normality of the corresponding counting measure, and if [{[W.sub.n]}.sub.n] is a sequence of enlarging bounded convex windows of observation, then
The possible breakdown in the asymptotic normality of [square root of (T)][??] is the reason why in Lemma 2 we report the asymptotic distribution of [square root of (T)]P'[U.sup.1/2][??] which always has a non-degenerate asymptotic normal distribution.
[P-values are computed assuming asymptotic normality.] IPS W-Statistic P-value Total Taxes -8.915 0.000 Property Tax -5.217 0.000 Total Sales & Gross Receipts Tax -6.440 0.000 Individual Income Tax -6.049 0.000 Corporate Net Income Tax -5.488 0.000 Total Income Tax -5.880 0.000 Direct General Expenditure -4.185 0.000 Education Expenditure -7.089 0.000 Public Welfare Expenditure 2.295 0.989 Health & Hospital Expenditure -2.893 0.002 Highway Expenditure -6.850 0.000 Table A2: Results of LLC Panel Unit Root Test on Share of Personal Income.
Y., Consistency and uniformly asymptotic normality of wavelet estimator in regression model with assoeiated samples, Statist.
He discusses the role of expansions and asymptotics in statistics, the basic properties of power series and asymptotic series, the study of rational approximations to functions, and various applications, such as the use of the delta method for bias reduction, variance stabilization, and the construction of normalizing transformations, with a focus on asymptotic normality and efficiency of standard estimators.
Before stating our result, we mention that the asymptotic normality of [X.sub.n] (in the sense of convergence in distribution) was first proved in [35] by a complex-analytic approach; for other approaches, see [59] (martingale difference), [31] (method of moments), [52] (contraction method).
In any case one can invoke the Central Limit Theorem for asymptotic normality because the sample size is large.
and, using a generalized Polya urn (see Section 2 and Remark 2.6) the asymptotic normality
H., 1973, On the Asymptotic Normality of the Maximum-Likelihood Estimate When Sampling From a Stable Distribution, Annals of Statistics, 1: 948-957.
GMTs of antibody and their confidence intervals were computed by transforming the results to a logarithmic scale, assuming asymptotic normality conditions were satisfied on the scale and converting back to the original scale.
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